Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves

Understand

We extend the Keldysh technique to enable the computation of out-of-time order correlators.

• We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions.
• At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves.
• The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics.